Homogeneous studies of transiting extrasolar planets III. Additional planets and stellar models

Transcription

1 Mon. Not. R. Astron. Soc. 408, (2010) doi: /j x Homogeneous studies of transiting extrasolar planets III. Additional planets and stellar models John Southworth Astrophysics Group, Keele University, Staffordshire ST5 5BG Accepted 2010 June 22. Received 2010 June 22; in original form 2010 April 16 ABSTRACT I derive the physical properties of 30 transiting extrasolar planetary systems using a homogeneous analysis of published data. The light curves are modelled with the JKTEBOP code, with special attention paid to the treatment of limb darkening, orbital eccentricity and error analysis. The light from some systems is contaminated by faint nearby stars, which if ignored will systematically bias the results. I show that it is not realistically possible to account for this using only transit light curves: light-curve solutions must be constrained by measurements of the amount of contaminating light. A contamination of 5 per cent is enough to make the measurement of a planetary radius 2 per cent too low. The physical properties of the 30 transiting systems are obtained by interpolating in tabulated predictions from theoretical stellar models to find the best match to the light-curve parameters and the measured stellar velocity amplitude, temperature and metal abundance. Statistical errors are propagated by a perturbation analysis which constructs complete error budgets for each output parameter. These error budgets are used to compile a list of systems which would benefit from additional photometric or spectroscopic measurements. The systematic errors arising from the inclusion of stellar models are assessed by using five independent sets of theoretical predictions for low-mass stars. This model dependence sets a lower limit on the accuracy of measurements of the physical properties of the systems, ranging from 1 per cent for the stellar mass to 0.6 per cent for the mass of the planet and 0.3 per cent for other quantities. The stellar density and the planetary surface gravity and equilibrium temperature are not affected by this model dependence. An external test on these systematic errors is performed by comparing the two discovery papers of the WASP-11/HAT-P-10 system: these two studies differ in their assessment of the ratio of the radii of the components and the effective temperature of the star. I find that the correlations of planetary surface gravity and mass with orbital period have significance levels of only 3.1σ and 2.3σ, respectively. The significance of the latter has not increased with the addition of new data since Paper II. The division of planets into two classes based on Safronov number is increasingly blurred. Most of the objects studied here would benefit from improved photometric and spectroscopic observations, as well as improvements in our understanding of low-mass stars and their effective temperature scale. Key words: binaries: eclipsing binaries: spectroscopic stars: fundamental parameters planetary systems. 1 INTRODUCTION The study of extrasolar planets is scientifically and culturally important, and after a late start (Mayor & Queloz 1995) the number of known planets is escalating rapidly. 1 Transiting planets are the crown jewels of this population as, with the exception of our own jkt@astro.keele.ac.uk 1 See the Extrasolar Planets Encyclopædia, Solar system, they are the only planets whose masses and radii are directly measurable. In addition to this, it is possible to put constraints on the properties of their atmospheres, in which much interesting physics occurs, through measurements of the depths of transits and occultations at different wavelengths. Whilst transiting extrasolar planets (TEPs) offer unique scientific possibilities, their study involves several complications. The most significant is that it is not in general possible to measure the mass and radius of a planet through basic observations alone. Additional constraints are needed, and are usually provided by forcing the C 2010 The Author. Journal compilation C 2010 RAS

2 1690 J. Southworth properties of the host stars to match theoretical expectations. 2 This introduces not only a model dependence (i.e. systematic error), but also the possibility of inconsistent results if different theoretical predictions are used for some TEPs. Systematic errors can blur any distinctions between planets, making it hard to pick out discrete groups of TEPs from the varied general population. This systematic error cannot be abolished, but it can at least be standardized. In this series of papers I am analysing the known transiting systems using rigorously homogeneous methods, with the aim of removing the systematic differences in measurements of the physical properties of TEPs. The resulting physical properties are therefore statistically compatible, and any structure in distributions of parameters is maximized. In Southworth (2008, hereafter Paper I) I analysed the light curves of the 14 transiting systems for which high-precision photometry was then available, paying careful attention to the role of limb darkening (LD) and to the estimation of comprehensive error bars. Southworth (2010, hereafter Paper II) used these results plus the predictions of three different theoretical stellar models to measure the physical properties of the 14 TEPs. In this work I broaden the analysis to 30 TEPs and five sets of theoretical stellar models, resulting in improved statistics and better systematic error estimates. There are a few homogeneous analyses of transiting systems available in the literature. A good analysis of 23 systems was presented by Torres, Winn & Holman (2008, hereafter TWH08), but these authors tried only two different theoretical model sets and did not assign systematic errors to their results. Analogously, such work would also benefit from homogeneous analysis of the spectra of the host stars in order to put their effective temperature and chemical abundance measurements on a consistent scale. Steps towards this goal were pioneered by Valenti & Fischer (2005) and are being continued by Ammler-von Eiff et al. (2010) and Ghezzi et al. (2010), but a homogeneous study of the host stars of all known TEPs is not currently available. In Section 2 I present the methods used to analyse the light curves of the 30 TEPs included in this work. Section 3 discusses the five theoretical stellar model sets and their application to determining the physical properties of the TEPs. Section 4 presents the new results for these objects, Section 5 discusses the influence of systematic errors due to the use of theoretical models and in Section 6 I summarize the physical properties of the known TEPs and explore correlations between various parameters. Those readers interested in the general properties of TEPs rather than specific systems can skip Section 4 without problem. 2 LIGHT-CURVE ANALYSIS: JKTEBOP I have modelled the light curves of each TEP using the JKTEBOP 3 code (Southworth, Maxted & Smalley 2004a,b). JKTEBOP grew out of the original EBOP program written for eclipsing binary star systems (Etzel 1981; Popper & Etzel 1981) and implementing the NDE model (Nelson & Davis 1972). JKTEBOP uses biaxial spheroids to model the component stars (or star and planet) so allows for departures from sphericity. The shapes of the components are governed by the mass ratio, q, although the results in this work are all extremely insensitive to the value of this parameter. The main parameters of a JKTEBOP fit are the orbital inclination, i, and the fractional radii of the two stars, 4 r A and r b. The fractional radii are defined as r A = R A a, r b = R b a, (1) where R A and R b are the stellar and planetary radii and a is the orbital semimajor axis. r A and r b correspond to radii of spheres of the same volume as the biaxial spheroids. In JKTEBOP the fractional radii are reparametrized as their sum and ratio: r A + r b, k = r b = R b, (2) r A R A because these are only weakly correlated with each other. In general the orbital period, P orb, is taken from the literature and the time of transit mid-point, T 0, is included as a fitted parameter in each JKTEBOP run. 2.1 Treatment of limb darkening The LD of the star is an important nuisance parameter affecting transit light curves which can be parametrized using any of five LD laws in JKTEBOP. Wherever possible the LD coefficients are included as fitted parameters, but when there is insufficient information for this the coefficients are fixed at theoretical values. For each light curve I have obtained solutions with each of the five LD laws (see Paper I for their definition) and with both LD coefficients fixed, with the linear coefficient fitted and the non-linear coefficient fixed (hereafter referred to as LD fit/fix ), and with both coefficients fitted. Theoretical LD coefficients have been taken from Van Hamme (1993), Claret (2000, 2004b) and Claret & Hauschildt (2003). The tabulated values have been bilinearly interpolated, using the JKTLD code, 5 to the known effective temperature (T eff ) and surface gravity (log g) of the star. I find that there is usually a spread of in the theoretical LD coefficients for cool stars, so when the non-linear LD coefficient is not included as a fitted parameter it is perturbed in the Monte Carlo simulations by ±0.1 on a flat distribution to account for this. The dependence on theoretical calculations in this case is still exceptionally small, because the linear and non-linear coefficients of the LD laws are highly correlated with each other (Southworth, Bruntt & Buzasi 2007a). Once solutions have been obtained for the five LD laws, the final result is calculated by taking the weighted means of the parameter values for the four two-parameter LD laws (i.e. the linear law is not used). The parameter error bars are taken to be the largest of the individual error bars (see below) plus a contribution to account for scatter of the parameter values from different LD law solutions. 2.2 Error analysis For each solution I run 1000 Monte Carlo simulations (Southworth et al. 2004c, 2005) to provide robust estimates of the 1σ statistical error bars. The starting parameter values are perturbed for each simulation to avoid sticking artificially close to the original best fit. 2 In principle, astrometric observations could either replace radial velocity measurements, or augment them and thus provide the missing constraint, but this has not yet been achieved in practise. 3 JKTEBOP is written in FORTRAN77 and the source code is available at jkt/codes/jktebop.html 4 Throughout this work stellar parameters are indicated by a subscripted A and planet parameters by a subscripted b, to conform to IAU nomenclature. 5 JKTLD is written in FORTRAN77 and the source code is available at jkt/codes/jktld.html

3 Studies of transiting extrasolar planets III 1691 If the reduced χ 2 of the fit, χν 2, is greater than unity, the Monte Carlo error bars are multiplied by χν 2 to account for this. Monte Carlo simulations do not fully account for the presence of correlated ( red ) noise, which is an unavoidable reality in highprecision light curves of bright stars. I therefore also run a residual permutation (or prayer bead ) algorithm (Jenkins, Caldwell & Borucki 2002) with the quadratic LD law. If there is significant correlated noise the residual permutation error bars will exceed the Monte Carlo error bars. I then take the larger of the two error estimates to represent the final error bars of the photometric parameters. 2.3 Orbital eccentricity Some TEPs have a non-circular orbit which must be accounted for in the light-curve analysis. Orbital eccentricity is very difficult to detect from the shape of a transit light curve (Kipping 2008) but can have a significant effect on the resulting parameters (for an example see Section 4.13). Non-circular orbits normally become apparent from radial velocity (RV) measurements of the parent stars. These RVs can then be used to determine the eccentricity, e, and the longitude of periastron, ω, of the binary orbit. JKTEBOP has been modified to account for orbital eccentricity by including the possibility of specifying values for either e and ω or the combinations e cos ω and e sin ω. These values and their uncertainties are then simply treated as extra observations, and e and ω (or their combinations) are included as fitted parameters. In this way the uncertainties in e and ω are correctly propagated into the error bars in the other photometric parameters. I prefer to work with e cos ω and e sin ω rather than e and ω, because the latter two quantities are strongly correlated with each other (e.g. Bruntt et al. 2006). 2.4 Contaminating light It is possible for additional light to contaminate photometric observations of transiting planets. Any extra light from nearby faint stars will dilute the transit depth, causing a systematic error in the light-curve parameters. This idea is becoming more important for several reasons. First, the Convection, Rotation and planetary Transits (CoRoT) satellite has a large point spread function (PSF) which usually contains a number of stars aside from the one hosting a transiting planet. Secondly, observations using telescope defocusing are potentially more susceptible to contaminating light. Thirdly, Daemgen et al. (2009) have detected faint companions to three transiting systems (TrES-2, TrES-4 and WASP-2) from groundbased high-resolution observations of 14 TEPs obtained with a lucky imaging camera. These companions could be bound to their respective transiting systems, or may just be asterisms. Temporarily ignoring the orbital ephemeris (P orb and T 0 ), there are three main observables in a transit shape: its depth, duration and the duration of totality (Paper I). From transit light curves we measure three quantities, which in the case of JKTEBOP are r A, r b and i. It is therefore expected to be impossible to fit directly for contaminating light, as this would require measuring four independent parameters using only three observables. This expectation will now be verified The effect of third light I have explored the possibility of measuring contaminating light by simulating a set of light curves with reasonable parameters Figure 1. Plot of the variation of parameters fitted to a set of synthetic transit light curves with 1 mmag of Gaussian noise added. The synthetic data sets were generated for a range of third light values but fitted with the assumption of L 3 = 0. Dotted lines show the input parameter values for the synthetic light-curve calculations. (r A + r b = 0.1, k = 0.1, i = 87 ). I added contaminating light (by convention referred to as third light and expressed as a fraction of the total system light) by amounts ranging from L 3 = 0to 0.75 in steps of These were transformed into typical good ground-based light curves by retaining approximately 400 points within each transit and adding a Gaussian scatter with standard deviation 1 mmag. These synthetic light curves were then fitted with JKTEBOP under the assumption that L 3 = 0. The results (Fig. 1) show that the presence of L 3 results in systematic overestimates of r A and underestimates of r b and i. The bottom panel of Fig. 1 shows that the quality of the fit does not get worse as L 3 increases. Unaccounted third light therefore biases the resulting parameters without being detectable through its impact on the quality of the fit. As a second test I modelled the same synthetic light curves again, this time fitting for third light. The resulting values of L 3 are shown in Fig. 2 and are extremely scattered as well as biased to smaller values. JKTEBOP deliberately does not restrict photometric parameters to physically realistic values (e.g. L 3 0), to avoid statistical biases in the uncertainties arising from Monte Carlo simulations. Fig. 2 demonstrates that there is a very small amount of information on L 3 in a good ground-based light curve, but that this information is far too sparse to be useful. Fig. 3 shows the resulting values of the other main parameters: r b and i are biased towards lower values and there is no trend visible in the sizes of the residuals. In reality a large value of L 3 is not expected because such a bright star would show up in the spectroscopic observations of a transiting

4 1692 J. Southworth of the spectroscopic observations) which almost exactly coincides with the planet host. As a guide, 5 per cent of third light can be compensated for by increasing r A by 1 per cent, and decreasing r b by 2 per cent and i by It can therefore change the derived radius of the planet by several per cent. Figure 2. Plot of fitted versus input values of third light for the same light curves as in Fig. 1, but with L 3 included as a fitted parameter. The dotted line shows parity. Note the large scale on the y-axis. Figure 3. Plot of the variation of parameters fitted to the same light curves as in Fig. 1, but in this case with L 3 included as a fitted parameter. The dotted lines show parity. system. Fainter stars can be found via high-resolution imaging if they are slightly away from the planet host star (Daemgen et al. 2009). However, it may never be possible to rule out the presence of a much fainter star (L 3 < 5 per cent depending on the quality Accounting for third light The observations of Daemgen et al. (2009) make it possible to account for third light when analysing transit light curves. They measured magnitude differences (light ratios) in the Sloan Digital Sky Survey (SDSS) i and z passbands. When necessary I have propagated the light ratios to other passbands by convolving synthetic spectra from ATLAS9 model atmospheres (Kurucz 1979, 1993) with passband response functions made available by the Isaac Newton Group. 6 Armed with L 3 values for the correct passbands, I have included these in the same way as e and ω. JKTEBOP was modified to accept measured L 3 values as observations, and L 3 was included as a fitted parameter. Note that several published studies have instead simply subtracted L 3 from a light curve before analysis, which is statistically incorrect as it neglects the uncertainty in L 3. Daemgen et al. (2009) surveyed 14 transiting systems and detected faint companions to three of them. The companions are within arcsec of the transit host stars, and are fainter by generally 4 mag in the i band. Daemgen et al. found that their presence changed the physical properties of the TEPs by roughly 1σ.Of the three affected objects, TrES-2 and TrES-4 are analysed in the current work and WASP-2 is the subject of a separate publication (Southworth et al. 2010). 3 INCORPORATING STELLAR MODELS: ABSDIM Analysis of a transit light curve gives the quantities r A, r b and i. 7 From RV measurements of the parent star it is possible to obtain e, ω and the velocity amplitude of the star, K A. With these observables we remain unfortunately one piece of information short of being able to calculate the full physical properties of the system. An additional constraint is needed, and this is generally supplied by forcing the properties of the star to match the predictions of theoretical stellar evolutionary models. To guide this process we can use the spectroscopically measured T eff and metal abundance, [Fe/H], of the star. In the current work I adopt the method outlined in Paper II, in which the variable governing the solution process is taken to be K b, the orbital velocity amplitude of the planet. An initial value of K b is defined, usually in the region of 150 km s 1, and the full physical properties of the system are calculated using standard formulae (e.g. Hilditch 2001). Armed with the resulting stellar mass, M A, and [Fe/H], I linearly interpolate within tabulated theoretical model results to find the predicted radius and T eff of the star. This process is iteratively repeated whilst varying K b in order to minimize the figure of merit: ( / ) fom = r(obs) A R (pred) 2 A a ( ) + T (obs) eff T (pred) 2 eff ( ) (3) σ σ r (obs) A T (obs) eff From transit light curves we also get P orb and T 0. The uncertainty in P orb is generally negligible, and T 0 does not enter the ABSDIM analysis.

5 Studies of transiting extrasolar planets III 1693 Table 1. Physical ingredients and coverage of the stellar models used in this work. Y ini is the primordial helium abundance, Y/ Z is the helium-to-metals enrichment ratio, Z is the solar metal abundance (fraction by mass) and α MLT is the mixing length parameter. Model set Reference Range in Range in metal Y ini Y/ Z Z α MLT Notes mass (M ) abundance (Z) Claret Claret (2004a, 2005, 2006, 2007) Calculated on request Y 2 Demarque et al. (2004) Teramo Pietrinferni et al. (2004) VRSS VandenBerg, Bergbusch & Dowler (2006) DSEP Dotter et al. (2008) which results in the best-fitting system properties. In principle it is possible to also solve for the age of the system, but in practise the wide variety of evolutionary time-scales of stars make this difficult. I therefore step through the possible ages of the star in 0.1 Gyr increments, starting at zero age and finishing when the star leaves the main sequence, in order to find the best overall solution. I do not make any attempt to match spectroscopically measured log g values as they are usually much less reliable than the surface gravity of the star calculated from the M A and R A obtained above. The above procedure implicitly applies the strong constraint on stellar density obtained from the light-curve analysis (Seager & Mallén-Ornelas 2003). The uncertainties in the system properties are calculated by a perturbation analysis, in which each input parameter is modified by its 1σ uncertainty and new solutions specified. The uncertainty for each output parameter is then calculated by adding the uncertainties due to each input parameter in quadrature. This perturbation analysis has the advantage of yielding detailed error budgets, where the effect of the uncertainty of every input parameter on every output parameter is specified. These error budgets indicate what additional observations are the best for improving our understanding of a specific TEP. 3.1 Which stellar models to use? As outlined above, the physical properties of TEPs are calculated by forcing the properties of the parent star to match theoretical expectations. This dependence on theoretical predictions is a concern and will cause a systematic error. It is well known that whilst theoretical models are pretty good at reproducing the actual properties of stars, the various model sets are not flawless and do not agree perfectly with each other. The existence of different theoretical model sets for low-mass stars opens the possibility of using several of them and explicitly deducing the systematic errors in TEP properties caused by their use. In Paper II six different sets of theoretical models were investigated and three adopted for calculating the planet properties. The Siess and Cambridge-2007 models were in relatively poor agreement with other models, and the Cambridge-2000 models had a lower coverage of the relevant parameter space than other models. I was therefore left with only three different model sets, which was insufficient to define high-quality systematic error estimates. On top of this, the Padova models included heavy element abundances only up to Z = 0.03 so did not cover quite a few transiting systems. In the current paper I have therefore adopted the same solution procedure as introduced in Paper II, but with a significantly revised data base of theoretical model predictions and with one more change. Instead of using the Claret models to define my baseline solutions and two other model sets to obtain systematic error estimates, I have used the unweighted mean and standard deviation of the results from all five model sets to describe the baseline solutions and systematic errors. The dependence of the final results on a single model set is therefore broken: all five model sets are treated equally and the choice of which sets of models to use becomes less important. Of the sets of theoretical models included in Paper II, only the Y 2 models survive unchanged here (see Table 1). The Claret models have been supplemented by additional calculations for higher metal abundances of Z = 0.06 and The third model set used here is Teramo 8 (Pietrinferni et al. 2004), and I selected the ones with moderate convective core overshooting (for masses >1.1 M ), the standard mass-loss law (η = 0.4) and normal elemental abundances (scaled-solar, i.e. no enhancement of the α-elements). For the fourth model set I acquired the Victoria Regina (VRSS) models 9 (VandenBerg et al. 2006) with scaled-solar elemental abundances. In these models the convective core overshooting parameter depends on mass and is empirically calibrated. The fifth and final model set (DSEP) comes from Dartmouth Stellar Evolution Database 10 and again comprises the calculations with scaled-solar elemental abundances. I selected those models which follow the standard heliumto-metal enrichment law. The DSEP models include a contraction to the zero-age main-sequence (ZAMS) which can take tens of Myr. In Fig. 4 I compare the predictions in mass and radius of the five sets of stellar models, for an age of 0.5 Gyr and for the adopted solar chemical composition (which differs between models). The models have a fairly good agreement in the mass radius plane, particularly near 1.0 M as they are calibrated on the Sun, but a wider variety in the mass T eff plane. Also shown in Fig. 4 are the masses, radii and T eff values of the sample of detached eclipsing binary star systems constructed in Paper II. It can be seen that the disagreement with the models is much larger than the error bars. This conclusion holds for all chemical compositions for which the five sets of models are available. Similarly, adopting an age either before or beyond the main sequence can provide an agreement for individual eclipsing binaries, but not for all of them simultaneously. Fig. 4 illustrates what can be expected for the variation of systematic errors with mass. The models agree with each other very well in some regions, so systematics will be minimized, and less well at lower and higher masses, when systematics will be larger. The agreement between models is clearly much better than with the properties of well-studied eclipsing binaries. This means that using the five model sets will lead to only a lower limit on the systematic errors in the properties of TEPs. A probable upper limit to the 8 Obtained from the BaSTI database on 2009 November 17: albione.oa-teramo.inaf.it/ 9 Obtained on 2009 November 18 from nrc-cnrc.gc.ca/cvo/community/victoriareginamodels/ 10 Obtained on 2009 November 18 from models/index.html

6 1694 J. Southworth Figure 4. Mass radius (left) and mass T eff (right) plots showing the predictions of the five sets of stellar models adopted in this work (solid lines). The predictions are for an age of 0.5 Gyr (to minimize the effects of evolution to and from the ZAMS) and for the solar chemical composition (which varies between models). The measured masses, radii and T eff values of a sample of detached eclipsing binaries (see Paper II) are shown for comparison, using blue error bars. The Sun is indicated by the usual ; note that the predictions of the models do not pass through the solar values on these plots as the Sun is much older than 0.5 Gyr. systematic effects can be obtained by calculating solutions with an eclipsing binary mass radius relation instead of a stellar model set; this is applied below and discussed further in Paper II. 3.2 Calculating the physical properties of transiting planets Using the method and theoretical stellar models outlined above, the mass, radius, surface gravity and mean density of the star (M A, R A, log g A, ρ A ) and of the planet (M b, R b, g b, ρ b ) can be calculated. For each TEP I have obtained results for each of the five stellar model sets and also using an empirical mass radius relation defined by the eclipsing binaries. The final result for each parameter is the unweighted mean of the five stellar-model results. The statistical error bar is taken to be the largest one from these five solutions and the systematic error bar is taken to be the standard deviation of the parameter values from the five solutions. I include the final K b value when possible to aid the comparison between different solutions for the same planet. K b is the parameter through which all of the stellar model dependence enters. The surface gravity of the planet, g b, can be calculated from purely geometrical observed quantities (Southworth, Wheatley & Sams 2007b) so has no systematic error. Similarly, the stellar density, ρ A, is independent of the stellar models (Seager & Mallén- Ornelas 2003) if M A M b is assumed. In addition to the above parameters, I have also calculated the equilibrium temperature (T eq ) and Safronov (1972) number ( ) of the planet. T eq is given by the equation ( ) 1 A 1/4 ( ) 1/2 RA T eq = T eff, (4) 4F 2a where A is the Bond albedo and F is a heat redistribution factor. Because A and F are not known precisely I instead calculate a modified equilibrium temperature (T eq ) which equals T eq if A = 1 4F: ( ) 1/2 T eq = T RA ( ra ) 1/2 eff = T eff. (5) 2a 2 The Safronov number is defined as the ratio of the escape velocity to the orbital velocity of the planet: = 1 ( ) 2 ( )( ) Vesc a Mb = = 1 M b. (6) 2 V orb R b M A r b M A From equation (5) above it can be seen that T eq depends only on the stellar T eff and the fractional radius obtained from the lightcurve analysis. T eq therefore turns out (like g b) to be independent of the stellar models, but does have some systematic error as it is dependent on the effective temperature scale of low-mass (F, G and K) stars. 4 RESULTS FOR INDIVIDUAL SYSTEMS In this section I present the photometric (JKTEBOP) and absolutedimensions (ABSDIM) analyses of a set of 30 TEPs based on highquality data. In many cases I adopt the JKTEBOP results from Paper I or later works (Southworth et al. 2009a,b,c, 2010). The final JKTEBOP results of all TEPs are collected in Table 2, which also includes the orbital periods and indicates for which systems a non-circular orbit was adopted. The mass ratio of each TEP is required as an input parameter for the light-curve analysis, but in all cases its effect on the solution is negligible. Representative values have been taken from the literature but will not be discussed further. The physical properties of all 30 TEPs are obtained or revised in the current work, using the new theoretical model sets discussed in Section 3. This also requires T eff,[fe/h]andk A values for each

7 Studies of transiting extrasolar planets III 1695 Table 2. Parameters from the light-curve analyses presented here and in previous works, and used here to determine the physical properties of the TEPs. The orbital periods are taken from the literature, and the bracketed numbers represent the uncertainty in the preceding digits. Systems for which orbital eccentricity was accounted for are indicated with a in the column marked e?. System Orbital period e? Orbital inclination, Fractional stellar Fractional planetary Reference (d) i ( ) radius, r A radius, r b GJ (76) ± ± ± Paper I HAT-P (93) ± ± ± This work HAT-P (61) 85.9 ± ± ± This work HD (25) 88.0 ± Paper I HD (80) ± ± ± Paper I HD (38) ± ± ± Paper I OGLE-TR (4) ± ± ± Paper I OGLE-TR (1) 79.8 ± ± ± Paper I OGLE-TR (41) ± ± ± Paper I OGLE-TR (13) 87.7 ± ± ± This work OGLE-TR (3) 83.3 ± ± ± Paper I OGLE-TR (1) 84.3 ± ± ± This work OGLE-TR (3) 88.0 ± This work OGLE-TR-L (7) ± ± ± This work TrES (6) ± ± ± Paper I TrES (18) ± ± ± This work TrES (5) ± This work TrES (75) ± ± ± This work WASP (18) 88.0 ± Paper I WASP (39) ± ± ± Southworth et al. (2010) WASP (2) 84.1 ± ± ± This work WASP (61) 89.0 ± Southworth et al. (2009b) WASP (13) 85.8 ± ± ± Southworth et al. (2009a) WASP (10) ± ± ± This work WASP (44) 85.0 ± ± ± Southworth et al. (2009c) XO (28) ± ± ± Paper I XO (16) 88.8 ± This work XO (32) ± ± ± This work XO (2) This work XO (11) ± ± ± This work system. These are summarized in Table 3. The values are mostly unchanged for the 14 TEPs studied in Paper II, but in a few cases improved values have become available and replace the previous entries. In Papers I and II the individual systems were tackled roughly in order of increasing complexity. The current work reverts to the more structured approach of attacking the TEPs in alphabetical order, beginning with those objects for which a light-curve analysis is presented (Sections 4.1 to 4.15), then moving on to those whose photometric parameters are adopted unchanged from Paper I (Section 4.16). 4.1 HAT-P-1 HAT-P-1 was found to be a TEP by Bakos et al. (2007a) from data taken by the HAT survey (Bakos et al. 2002, 2004). Its low mass (0.5M Jup ) and large radius (1.2R Jup ) make it one of the least dense exoplanets known. Excellent light curves from the FLWO 1.2-m (z band), Lick 1.0-m Nickel (Z band) and Wise 1.0-m telescopes were presented by Winn et al. (2007c) and the first two of these were included in Paper I. Since then additional data from the Nickel (Z band) and the Hawaiian 2-m Magnum (V band) telescopes have been obtained by Johnson et al. (2008). In this work I have analysed the latter two data sets in order to refine the results from Paper I. In both cases I have adopted solutions with the linear LD coefficient fitted and the non-linear coefficient fixed but perturbed in the Monte Carlo simulations ( LD fit/fix ). The residual permutation analyses indicate that correlated errors are important for both data sets. The final light-curve parameters are the weighted means of those for the four studied data sets. The results agree well with each other except for k, for which χν 2 = 2.8. The error bar for k has been multiplied by 2.8 to account for this. The light-curve fits are plotted in Fig. 5 and summarized in Table A3. They are in good agreement with literature values. The physical properties of HAT-P-1 have been calculated using the five different sets of stellar evolutionary models plus the empirical mass radius relation from Paper II. The individual solutions are given in Table A4 and then compared with literature values, where a good agreement is found. 4.2 HAT-P-2 HAT-P-2 was discovered to be a TEP system by Bakos et al. (2007b), under the name HD It is a very bright system (V = 8.7) with a massive planet (M b = 8.74M Jup ) in a highly eccentric orbit. It has been found not to exhibit a spin orbit misalignment (Winn et al. 2007a; Loeillet et al. 2008), in contrast to other massive TEPs on eccentric orbits (Johnson et al. 2009a). Good z-band light curves of HAT-P-2 have been published by Bakos et al. (2007b), covering one transit with the FLWO 1.2 m, and by Pál et al. (2010), covering another six transits with the FLWO 1.2 m and the Perkins telescopes. Here I analyse the FLWO data sets

8 1696 J. Southworth Table 3. Measured quantities for the parent stars which were adopted in the analysis presented in this work. System Velocity amplitude (m s 1 ) T eff (K) Reference [ Fe H ] Reference GJ ± 0.52 Maness et al. (2007) 3500 ± 100 Bean, Benedict & Endl (2006) 0.03 ± 0.2 Bonfils et al. (2005) HAT-P ± 1.4 Johnson et al. (2008) 5975 ± 50 Bakos et al. (2007a) 0.13 ± 0.05 Bakos et al. (2007a) HAT-P ± 17.2 Pál et al. (2010) 6290 ± 60 Pál et al. (2010) 0.14 ± 0.08 Pál et al. (2010) HD ± 1.2 Sato et al. (2005) 6147 ± 50 Sato et al. (2005) 0.36 ± 0.05 Sato et al. (2005) HD ± 0.88 Boisse et al. (2009) 5050 ± 50 Bouchy et al. (2005b) 0.03 ± 0.05 Bouchy et al. (2005b) HD ± 1.0 Naef et al. (2004) 6117 ± 50 Santos, Israelian & Mayor (2004) 0.02 ± 0.05 Santos et al. (2004) OGLE-TR ± 17 Konacki et al. (2005) 6075 ± 86 Santos et al. (2006) 0.28 ± 0.10 Santos et al. (2006) OGLE-TR ± 22 Bouchy et al. (2005a) 6119 ± 62 Santos et al. (2006) 0.25 ± 0.08 Santos et al. (2006) OGLE-TR ± 14 Pont et al. (2004) 5044 ± 83 Santos et al. (2006) 0.19 ± 0.07 Santos et al. (2006) OGLE-TR ± 34 TWH ± 106 Santos et al. (2006) 0.15 ± 0.10 Santos et al. (2006) OGLE-TR ± 18 Moutou et al. (2004) 6210 ± 59 Gillon et al. (2007) 0.37 ± 0.07 Gillon et al. (2007) OGLE-TR ± 17 Pont et al. (2008) 5924 ± 64 Pont et al. (2008) 0.37 ± 0.08 Pont et al. (2008) OGLE-TR ± 16 Udalski et al. (2008) 6325 ± 91 Udalski et al. (2008) 0.11 ± 0.10 Udalski et al. (2008) OGLE-TR-L9 510 ± 170 Snellen et al. (2009) 6933 ± 58 Snellen et al. (2009) 0.05 ± 0.20 Snellen et al. (2009) TrES ± 6.2 Alonso et al. (2004) 5226 ± 50 Santos et al. (2006) 0.06 ± 0.05 Santos et al. (2006) TrES ± 2.6 O Donovan et al. (2006) 5795 ± 73 Ammler-von Eiff et al. (2009) 0.06 ± 0.08 Ammler-von Eiff et al. (2009) TrES ± 11 Sozzetti et al. (2009) 5650 ± 75 Sozzetti et al. (2009) 0.19 ± 0.08 Sozzetti et al. (2009) TrES ± 7.2 Mandushev et al. (2007) 6200 ± 75 Sozzetti et al. (2009) 0.14 ± 0.09 Sozzetti et al. (2009) WASP ± 9 Wheatley et al. (2010) 6110 ± 50 Stempels et al. (2007) 0.23 ± 0.08 Stempels et al. (2007) WASP ± 3.0 Triaud et al. (2010) 5150 ± 80 Triaud et al. (2010) 0.08 ± 0.08 Triaud et al. (2010) WASP ± 9.5 Tripathi et al. (2010) 6400 ± 100 Pollacco et al. (2008) 0.00 ± 0.20 Pollacco et al. (2008) WASP Triaud et al. (2010) 5500 ± 100 Gillon et al. (2009) 0.03 ± 0.09 Gillon et al. (2009) WASP ± 1.8 Triaud et al. (2010) 5700 ± 100 Gillon et al. (2009) 0.09 ± 0.09 Gillon et al. (2009) WASP ± 7.5 Johnson et al. (2009b) 4675 ± 100 Christian et al. (2009) 0.03 ± 0.20 Christian et al. (2009) WASP ± 2.0 Triaud et al. (2010) 6400 ± 100 Hellier et al. (2009) 0.00 ± 0.09 Hellier et al. (2009) XO ± 9.0 McCullough et al. (2006) 5750 ± 50 McCullough et al. (2006) 0.02 ± 0.05 McCullough et al. (2006) XO-2 85 ± 8 Burke et al. (2007) 5340 ± 50 Burke et al. (2007) 0.45 ± 0.05 Burke et al. (2007) XO ± 10 Winn et al. (2009) 6429 ± 75 Johns-Krull et al. (2008) 0.18 ± 0.05 Johns-Krull et al. (2008) XO ± 16 McCullough et al. (2008) 6397 ± 70 McCullough et al. (2008) 0.04 ± 0.05 McCullough et al. (2008) XO ± 2.0 Pál et al. (2009) 5370 ± 70 Pál et al. (2009) 0.05 ± 0.06 Pál et al. (2009) together, omitting the small amount of data taken on the night of 2007 March 18, as well as the Perkins data. One complication is the orbital eccentricity: this was accounted for using the method discussed in Section 2.3 and adopting the constraints e cos ω = ± and e sin ω = ± (Pál et al. 2010). In both cases correlated errors were not important and the LD fit/fix solutions were adopted. The best fits are shown in Fig. 6. The two light-curve solutions unfortunately do not agree very well (9.3σ discrepancy in k). I therefore adopt the FLWO 1.2-m results, as these are the much more extensive of the two sets of data and have full coverage of the transit phases. The FLWO results agree well with those of Pál et al. (2010), for which most of the data come from, but have a larger r A and r b than other literature values (Table A7). As expected given the light-curve results, my ABSDIM analysis returns system properties in good agreement with those of Pál et al. (2010) but not with other literature studies (Table A8). The prime mover in the most recent solutions is r A, which has a strong effect on the density of the star and thus the other physical properties. The radius of the planet is uncertain by 10 per cent, despite the existence of a high-quality light curve for HAT-P-2, because the transit depth is shallow (0.6 per cent). An improved photometric study is warranted. 4.3 OGLE-TR-113 Like OGLE-TR-132 (studied in Paper I), OGLE-TR-113 was identified as a possible planetary system by Udalski et al. (2002) and its nature was confirmed by Bouchy et al. (2004) using the OGLE light curve and new RV measurements. It was independently confirmed as a TEP by Konacki et al. (2004), also from the OGLE light curve and high-precision RVs, and an abundance analysis of the parent star has been presented by Santos et al. (2006). Whilst OGLE-TR- 113 exhibits a deep transit, its photometric tractability is hindered by the presence of a brighter star only 3 arcsec away. Apart from the OGLE discovery observations (Udalski et al. 2002), three photometric studies of OGLE-TR-113 have been published. Gillon et al. (2006) used the ESO New Technology Telescope (NTT) and SUSI2 imager to observe two transits in the R band, and obtained what is currently the best light curve of OGLE-TR-113. Snellen & Covino (2007) observed a K-band transit and an occultation of the system using NTT/SOFI, and detected the occultation with a significance of 2.8σ.Díaz et al. (2007) obtained V-band photometry of one transit using a Very Large Telescope (VLT) and the Visible Multi-Object Spectrograph (VIMOS) instrument; additional data taken in the I and K s bands are unavailable and of lower quality. In this work I analyse the Gillon et al. observations, the Snellen & Covino transit light curve and the V-band data obtained by Díaz et al. For the second of these three data sets I allowed for light from the planet with a surface brightness ratio of 0.07 ± The surface brightness ratio is a parameter of the JKTEBOP model which is important for eclipsing binary systems but usually left at zero for transiting systems due to the faintness of the planet with respect to the star. The best fits are shown in Fig. 7 and given in Table A12. In all three cases correlated noise is not important. For the Snellen light curve I had to adopt solutions with both LD coefficients fixed, but for the other two I was able to use the LD fit/fix solutions. The final results for the Gillon and Snellen data are in good agreement. The solution of the Díaz data prefers a rather higher i and lower r A

9 Studies of transiting extrasolar planets III 1697 Figure 5. Phased light curves of HAT-P-1 compared to the best fits found using JKTEBOP and the quadratic LD law in Paper I and in this work. The best fits and residuals are offset from unity and zero fluxes, respectively, for display purposes. The light curves are, from top to bottom, FLWO z band (Winn et al. 2007c), Lick Z band (Winn et al. 2007c), Magnum V band (Johnson et al. 2008) and Nickel Z band (Johnson et al. 2008). and rb. I therefore combined the Gillon and Snellen data results to obtain the final light-curve parameters. The resulting physical properties of OGLE-TR-113 are given in Table A13. The system age is constrained only to be more than a few Gyr, and in several cases is up against the edge of the stellar model grid at 20 Gyr. Aside from that, the properties of the star and planet are rather well determined but would benefit from an improved K A value as well as a better light curve. The agreement with literature studies is good, although it seems that in some cases the published error bars are smaller than one would expect. The VLT light curve is analysed here and is rather affected by correlated noise. Including the linear LD coefficients as a fitted parameter gives substantially better fits than with both LD coefficients fixed, but the data cannot support the determination of both LD coefficients. I therefore adopt the LD fit/fix solutions (see Fig. 8 and Table A15), which are not in good agreement with Pont et al. (2008). Compared to these authors I find a solution with a lower i and a correspondingly larger star and planet. The physical properties of OGLE-TR-182 are summarized in Table A16 and point to a planet with a rather low density of 0.33ρ Jup. However, my results are rather different to those of Pont et al. (2008), and are in poorer agreement with the measured spectroscopic T eff and (rather uncertain) log g measurement. My analysis procedure is more sensitive to the quality of the light curve than the more global approach taken by Pont et al., so is potentially more susceptible to correlated noise. This possibility should be investigated by acquiring a new light curve, under good seeing conditions to cope with the crowded field. 4.4 OGLE-TR-182 OGLE-TR-182 is the sixth TEP discovered as a result of the OGLE search for light variability in selected fields in the Southern hemisphere. Its discovery and analysis was presented by Pont et al. (2008), which remains the only study of this object to date. OGLETR-182 is difficult because of its faintness (V = 16.8 and I = 15.9) and crowded field. Pont et al. (2008) obtained 24 RV measurements using VLT/Fibre Large Array Multi Element Spectrograph (FLAMES)/Ultraviolet and Visual Echelle Spectrograph (UVES), and a light curve with VLT/Focal Reducer and low dispersion Spectrograph 1 (FORS1). C C 2010 RAS, MNRAS 408, The Author. Journal compilation 4.5 OGLE-TR-211 OGLE-TR-211 is the seventh TEP discovered using OGLE data (Udalski et al. 2008). Its relative faintness means that the available follow-up photometry and spectroscopy is not definitive. The parent star is more massive and also more evolved than the Sun, which results in the transit being rather shallow (Fig. 9). Here I analyse the VLT light curve presented by Udalski et al. (2008), ignoring the observational errors supplied with the data which are quite discretized (the only values are 0.001, and 0.003) and contribute to instability in the light-curve solution. Figure 6. Phased z-band light curves of HAT-P-2 compared to the best fits found using JKTEBOP and the quadratic LD law. The best fits and residuals are offset for display purposes. The upper light curve is from the FLWO 1.2 m (Bakos et al. 2007b; Pa l et al. 2010) and the lower is from the Perkins 1.8 m (Pa l et al. 2010).

10 1698 J. Southworth Figure 7. Phased light curves of OGLE-TR-113 with the best fits found using JKTEBOP and the quadratic LD law and residuals of the fits. From top to bottom the data sets are Gillon et al. (2006) (R band), Snellen & Covino (2007) (K s band, binned by 5 for display purposes) and Díaz et al. (2007) (V band). Figure 8. Phased VLT light curve of OGLE-TR-182 from Pont et al. (2008) compared to the best fit found using JKTEBOP and the quadratic LD law. The residuals are offset from zero for display purposes. I am not able to get a determinate solution to the VLT data. Possible fits occupy a locus extending from a high i with low r A to a lower i with a large r A. I have therefore calculated solutions for a range of i values and retained only those which in the ABSDIM Figure 9. Phased VLT light curve of OGLE-TR-211 from Udalski et al. (2008) compared to the best fit found using JKTEBOP and the quadratic LD law. The residuals are offset from zero for display purposes. analysis result in a T eff within a conservative 3σ of the observed value. The observed stellar log g did not provide a useful constraint. Allowable solutions extend from i = 90 down to a sharp cut-off around i = so I present solutions for i = 86,88 and 90 in Table A17. For the final result I accept the LD fit/fix solutions for i = 88 but specify errors which account for both the Monte Carlo error bars and the variation between the different solutions (Table A18). The correlated errors are again important, as can be seen in Fig. 9. The physical properties of OGLE-TR-211 are shown in Table A19 and are in reasonable agreement with those of Udalski et al. (2008) except for the planetary mass. M b depends mainly on the measured K A, for which both studies have used the same value, so it is not clear why such a discrepancy should arise. Table A19 includes the first determinations of the age and density of the star, planetary equilibrium temperature (which is quite high at T eq = K) and Safronov number. The system age is relatively well determined ( Gyr) because the star has evolved away from the ZAMS. OGLE-TR-211 would certainly benefit from additional spectroscopic and photometric observations. 4.6 OGLE-TR-L9 OGLE-TR-L9 was discovered within the OGLE-II survey data (Udalski, Kubiak & Szymański 1997) by Snellen et al. (2009), and is a relatively massive planet orbiting a rapidly rotating (V sin i = 39 km s 1 ) F3 V star. High-quality follow-up light curves were obtained by Snellen et al. using the newly commissioned Gamma- Ray Burst Optical/Near-Infrared Detector (GROND) instrument (Greiner et al. 2008) on the 2.2-m telescope at ESO La Silla. GROND is a CCD imager which utilizes dichroics to observe simultaneously in seven passbands [SDSS griz and near-infrared (IR) JHK]. In the case of OGLE-TR-L9 the JHK data were too noisy to be useful, but the griz data are of good quality (Fig. 10). The griz observations have been analysed here (Tables A20 A23). The gri light curves are good enough to support LD fit/fix solutions but for the z data both LD coefficients were held fixed. The parameters for the four light curves were combined to obtain the